Math, asked by yashdeep8, 1 year ago

ffffffffiiiinnnnnnndddddd​

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Answered by B509
0

Answer:

Ok, I have done

Step-by-step explanation:

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Answered by A1111
0

We have :-

 =  > x^{2}  +  \frac{1}{ {x}^{2} }  = 51 \: \:  \: .....(1)

On multiplying equation (1) by x, we get :

 =   >   {x}^{3}  +  \frac{1}{x}  = 51x \\  \\  =  >  {x}^{3}  = 51x -  \frac{1}{x}  \:  \:  \: .....(2)

Similarly, on dividing equation (1) by x, we get :

 =  > x +  \frac{1}{ {x}^{3} }  =  \frac{51}{x}  \\  \\  =  >  \frac{1}{ {x}^{3} }  =  \frac{51}{x}  - x \:  \:  \: .....(3)

Now, subtract equation (2) and equation (3) :

 =  >  {x}^{3}   -   \frac{1}{ {x}^{3} }  = 51x -  \frac{1}{x}   -   \frac{51}{x}   +  x \\  \\  =  >  {x}^{3}   -   \frac{1}{ {x}^{3} }  = 51(x  -   \frac{1}{x} ) + (x  -   \frac{1}{x} ) \\  \\  =  >  {x}^{3}   -  \frac{1}{ {x}^{3} }  = 52(x  -  \frac{1}{x} ) \:  \:  \: .....(4)

Then,

 =  >  {x}^{2}  +  \frac{1}{ {x}^{2} } = 51 \\  \\  =  >   {x}^{2}  +  \frac{1}{x^{2} }    -  2 = 49 \\  \\  =  > (x  -  \frac{1}{x} )^{2}  = 49 \\  \\  =  > x  -   \frac{1}{x}  =  ± 7 \:  \:  \: .....(5)

Thus, from equations (4) and (5) :-

=> x³ - 1/x³ = 52(±7) = ± 364

Since, this method is quite a bit lengthy, you can also use the identity :-

a³ - b³ = (a - b)(a² + ab + b²)

Hope, it'll help you.....

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